In short, no to all questions.
Aside from manufacturer-provided utilities (in-camera or otherwise), there is no magic formula for correcting lens abberations in post, nor is there a straightforward way to do this in Photoshop aside from the Lens Correction filter, which has its limitations. Any non-standard lens mounting such as reversing mean that any 'auto' correction tools won't work, so you're left with anything you can pull off in Photoshop.
The abberations involved are not limited to just barrel/pincushion distortion which are basically all that Photoshop (and other apps') built in 'lens correction' filters can correct.
The notion that mounting identical lenses face to face with a reversing ring unfortunately doesn't mean that they correct each other's abberations, as nice as this would be if it were true. This is due to (practically) irreversible physical effects like diffraction and refraction.
Reversing a lens doesn't also reverse the distortion characteristics, it just changes it in unpredictable ways. Camera lenses are not designed to be reversed, so results will vary widely from lens to lens. However, you can generally expect wide lenses to exhibit more field curvature and spherachromatism than normal lenses when reversed (this is not the same thing as barrel/pincushion distortion though), but beyond that there's no golden rule regarding lens performance when reversed.